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Any number to the power zero is equal to one. That can be derived from the following index law:

xa*xb = xa+b (x not zero)

Now let b = 0 so that the above becomes

xa*x0 = xa+0

so

xa*x0 = xa (since a+0 = a)

That is, any number multiplied by x0 is the number itself. That can be true only if x0 is the multiplicative identity, that is, only if x0 = 1.

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Q: Why is 10 power 0 equal to 1?

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Recall that any number to the power 0 is always equal to 1. So 10^0 (read that as "10 to the power 0") equals 1. and 10^1 = 10 10^2 = 100 10^3 = 1000 10^4 = 10000. Notice something? 10^any integer = 1 followed by "any integer" zeroes. So, 10^100 = 1 followed by 100 zeroes. Oldsniper

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